The proposed research is directed towards a number of topics in the area of likelihood based statistical methods. One set of topics will involve the development of several new asymptotic methods in the area of parametric models, focussing on improved distributional properties in the presence of nuisance parameters and on testing methods for the number of components in a mixture. The second set of topics revolves around semiparametric and nonparametric inference in the mixture model, where the class of models needs to be expanded and further inferential methods need to be developed. The most widely used method for drawing statistical conclusions, called the method of maximum likelihood, is based on a mathematical version of the intuitive notion that the true value of a parameter will generally be found among those that seem "most likely" given the observed data. This powerful tool enables one to write down models for complex phenomenon and, by maximizing the likelihood, draw conclusions about the state of nature that generated the data. However, the likelihood method is not perfect, and the objective of this research proposal is to further its development, both in computation and in theory, in several areas of wide application.
